2-Dimensional
MotionVECTOR COMPONENTS AND ADDITION
PROJECTILES – HORIZONTAL AND ANGLED
Vectors – magnitude and direction
Drawn to scale
5m 15 m
Vector Addition: Vectors are drawn tip-to-tail
Expressed as 𝐴+ 𝐵
Where one vector ends, begin the next vector
The order doesn’t matter, but the size and direction does
The Resultant is the vector sum: draw it from beginning to end
R = 20 m
Vector Addition and Subtraction
Vector Subtraction
Expressed as 𝐴− 𝐵
Just means to change the direction of vector B by 180 degrees
R = 5-15 = 10 m
2-Dimensional Example
Splat the cat walks 5 m north, 15 m west, and 20 m north again.
What is the displacement?
𝑅 = 𝑥2 + 𝑦2
Coordinate Systems and Vector
Components
cos θ =𝑎𝑑𝑗
ℎ𝑦𝑝
sin 𝜃 =𝑜𝑝𝑝
ℎ𝑦𝑝
tan 𝜃 =𝑜𝑝𝑝
𝑎𝑑𝑗
Step 1: make a triangle
Use trig to find x and y
25 m at 30 deg
65 m/s at 250 deg
To Add Multiple Vectors: Example – An airplane flies 190 m/s at 25 degrees above the horizontal
against a wind that is 32 m/s at 30 degrees west of north. What is the
plane’s resultant velocity?
1. Resolve each vector into its components:
2. Total x components:
3. Total y components:
4. Sketch triangle using total x and y
Calculate Resultant:
Calculate angle using trig:
Relative Velocity
What is the velocity of A with respect to B?
Asks what the velocity of A would be, to YOU, if you were
on top of item B
Example: Splat the cat runs east at 3 m/s, while riding on a
train that also travels east at 22 m/s.
Splat’s velocity relative to ground:
Splat’s velocity relative to the train:
What if Splat turned and went west at 3 m/s?
What is his velocity NOW relative to ground:
What about relative to the train?
What if Splat runs north at 3 m/s?
Projectile Motion A projectile is anything that is given initial velocity but then is only
influenced by gravity
Examples: thrown football, tossed basketball, bullet shot from gun, cat
shot from cannon…
Projectiles have parabolic paths
Motion must be broken into x and y components!!
Remember : Gravity only acts in the y – direction!!
Constant Acceleration Projectile – x dir. Projectile – y dir.
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡
𝑣𝑓2 = 𝑣𝑖
2 + 2𝑎𝑥
𝑥 = 𝑣𝑖𝑡 +1
2𝑎𝑡2
𝑥 =1
2𝑣𝑖 + 𝑣𝑓 𝑡
Modeling Projectile Problems:
1. Always draw a picture
2. Label givens on the picture!
Example: Splat the cat is pushed out of a window that is 35.0
meters above the ground. If Splat lands 6.5 m away from the
building base, how fast was he going when he left the
window?
Step 1: Picture Step 2: Separate Givens into x and y
Step 2: Choose an equation! You cannot mix x and y givens!!!!!!!!
Full Parabola Problems:
1. Always draw a picture
2. Label givens on the picture